The world already knew that Donald Trump would be unlike any other US President we have seen in our lifetimes.

But who expected him to condemn the results of an election in which he emerged the winner? How can his claim that “millions of people” voted illegally do anything that undermine Americans’ confidence in their democratic system?

With the clock counting down towards Mr Trump enters the White House on January 20, here are five of the things we have learned about the man Theresa May and every other world leader will have to deal with.

1. He’s keeping his Twitter account active

When you’re President of the United States a joke or a muttered comment caught on a microphone can cause an international incident. That’s why presidential addresses are painstakingly scripted and why speechwriters and spokesman are on the White House team.

Donald Trump's Twitter profile

But Mr Trump’s Twitter “followers” love how he communicates directly with them and winning the election hasn’t stopped him shooting from the hip.

2. He is still willing to jump into political streetfights

George W Bush and Al Gore tried to stay above the fray when the result of the 2000 election hung in the balance and Democrats and Republicans tussled over the counting of the votes in Florida.

Mr Trump is on his way to the White House but he will not accept that he won in the all-important electoral college but that Hillary Clinton received more votes overall.

He declared: “In addition to winning the Electoral College in a landslide, I won the popular vote if you deduct the millions of people who voted illegally.”

It is a remarkable thing for a President-elect to allege that massive wrongdoing would account for Mrs Clinton’s lead of more than two million votes. He went on to claim there was “serious voter fraud in Virginia, New Hampshire and California” – states she won.

Such a claim, presented without evidence, can only make it harder for him to unify the country after the election, and will put new momentum behind the push for recounts in states he narrowly won.

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3. He does not like to be mocked

Saturday Night Live is a comedy show which has been a fixture of the American weekend since 1977 and is famed for the way it roasts political figures. Alec Baldwin gleefully impersonated Mr Trump throughout the election but the President-to-be shows little signs of relishing satire.

He complained on Twitter: “It is a totally one-sided, biased show – nothing funny at all. Equal time for us?”

If such interventions continue once he arrives in the Oval Office, will producers and comedians feel under pressure to smooth off the jagged edges of their jokes?

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5. He is more than happy to hand out advice - whether people want it or not

Not content with picking his own cabinet, he had some advice for the Prime Minister, declaring that “many people” would like to see Nigel Farage as Britain’s Ambassador to the United States.

He added: “He would do a great job!”

This astounding diplomatic intervention was a gift to Ukip (he had ruffled feathers by meeting Mr Farage in person after the election). It will not make Sir Kim Darroch’s task as ambassador any easier, knowing that Mr Trump would like to see him replaced.

Donald Trump meets Nigel Farage at Trump Tower

What does this tell us?

Donald Trump’s gracious acceptance speech fuelled speculation that as President the billionaire might prove a very character to the candidate whose rants in arenas and on Twitter electrified his fans.

There were warm words for Hillary Clinton, even though he had earlier suggested she should be behind bars. Might it be possible that his populist tub-thumping on the campaign trail was a theatrical act and in fact an urbane New Yorker is at the America’s helm?

Mr Trump can be charming and gracious. After routinely describing the New York Times as “failing” he met with senior figures on the newspaper and assured them he considered the title a “world jewel”.

New Yorkers react to the election of Donald Trump as president of the United States (Photo: Spencer Platt/Getty Images)

Millions of people might like to think he is much more moderate than he lets on, but the early indications are that he has no intention of pressing his mute button (if he has one). His appointment of Steve Bannon, a former executive with a right-leaning news website, as his chief strategist gives us no reason to think he will not continue to cultivate the populist forces that helped power his victory.

In the coming months and years Mr Trump has the opportunity to remake not just the presidency but the United States and its relations with the world. We are about to see what influence, if any, Britain’s so-called “special relationship” will have on his agenda.

If Mrs May wants to get through to him, perhaps the best way will be sending a Direct Message on Twitter.